Year: 2018
Type: article
Abstract: The multivariate multi-response (MVMR) linear regression problem is investigated, in which design matrices can be distributed differently across K linear regressions. The support union of K p-dimensional regression vectors are recovered via block regularized Lasso which uses the l1/l2 norm for regression vectors across K tasks. Sufficient and necessary conditions to guarantee successful recovery of the support union are characterized. More specifically, it is shown that under certain conditions on the distributions of design matrices, if n>cp1ψ(B∗,Σ(1:K))log(p−s) where cp1 is a constant and s is the size of the support set, then the l1/l2 regularized Lasso correctly recovers the support union; and if np2ψ(B∗,Σ(1:K))log(p−s) where cp2 is a constant, then the l1/l2 regularized Lasso fails to recover the support union. In particular, ψ(B∗,Σ(1:K)) captures the sparsity of K regression vectors and the statistical properties of the design matrices. Numerical results are provided to demonstrate the advantages of joint support union recovery using multi-task Lasso problem over studying each problem individually.
Source: Figshare
DOI: 10.1184/r1/6475490
Authors: Wang, Weiguang, Liang, Yingbin, P Xing, Eric
Institutions: Syracuse University, Carnegie Mellon University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2156543150